Properties

Label 729.2.i.a.685.4
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.4
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.02543 - 0.563818i) q^{2} +(2.07216 + 1.25056i) q^{4} +(1.27054 - 0.0493029i) q^{5} +(4.39851 + 0.687914i) q^{7} +(-0.606370 - 0.642715i) q^{8} +O(q^{10})\) \(q+(-2.02543 - 0.563818i) q^{2} +(2.07216 + 1.25056i) q^{4} +(1.27054 - 0.0493029i) q^{5} +(4.39851 + 0.687914i) q^{7} +(-0.606370 - 0.642715i) q^{8} +(-2.60120 - 0.616496i) q^{10} +(-0.0413646 - 0.302842i) q^{11} +(1.95043 - 2.84380i) q^{13} +(-8.52104 - 3.87329i) q^{14} +(-1.39012 - 2.63908i) q^{16} +(6.95270 - 3.49177i) q^{17} +(0.466686 + 8.01269i) q^{19} +(2.69443 + 1.48672i) q^{20} +(-0.0869667 + 0.636709i) q^{22} +(-1.39733 + 3.61918i) q^{23} +(-3.37311 + 0.262179i) q^{25} +(-5.55385 + 4.66024i) q^{26} +(8.25415 + 6.92605i) q^{28} +(-2.53701 - 1.81334i) q^{29} +(-2.85491 + 3.27137i) q^{31} +(1.70176 + 7.85622i) q^{32} +(-16.0510 + 3.15231i) q^{34} +(5.62241 + 0.657166i) q^{35} +(1.50445 + 2.02083i) q^{37} +(3.57246 - 16.4923i) q^{38} +(-0.802107 - 0.786701i) q^{40} +(0.728308 - 2.82746i) q^{41} +(-6.63437 - 6.02037i) q^{43} +(0.293007 - 0.679266i) q^{44} +(4.87077 - 6.54258i) q^{46} +(0.229710 + 0.263218i) q^{47} +(12.2079 + 3.91431i) q^{49} +(6.97985 + 1.37080i) q^{50} +(7.59793 - 3.45368i) q^{52} +(-0.771083 + 4.37303i) q^{53} +(-0.0674864 - 0.382735i) q^{55} +(-2.22499 - 3.24412i) q^{56} +(4.11614 + 5.10322i) q^{58} +(-2.57549 + 1.05221i) q^{59} +(10.2081 - 6.16060i) q^{61} +(7.62689 - 5.01629i) q^{62} +(0.635797 - 10.9162i) q^{64} +(2.33790 - 3.70933i) q^{65} +(5.48432 - 3.91995i) q^{67} +(18.7738 + 1.45921i) q^{68} +(-11.0173 - 4.50107i) q^{70} +(0.934287 + 3.12074i) q^{71} +(-4.31382 + 1.02239i) q^{73} +(-1.90779 - 4.94130i) q^{74} +(-9.05327 + 17.1872i) q^{76} +(0.0263870 - 1.36051i) q^{77} +(9.02377 - 8.85045i) q^{79} +(-1.89632 - 3.28453i) q^{80} +(-3.06932 + 5.31621i) q^{82} +(0.101470 + 0.393932i) q^{83} +(8.66155 - 4.77924i) q^{85} +(10.0431 + 15.9345i) q^{86} +(-0.169559 + 0.210220i) q^{88} +(-2.03708 + 6.80431i) q^{89} +(10.5353 - 11.1667i) q^{91} +(-7.42149 + 5.75209i) q^{92} +(-0.316855 - 0.662646i) q^{94} +(0.987994 + 10.1575i) q^{95} +(-11.4753 - 0.445293i) q^{97} +(-22.5194 - 14.8112i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.02543 0.563818i −1.43220 0.398680i −0.536711 0.843766i \(-0.680333\pi\)
−0.895488 + 0.445086i \(0.853173\pi\)
\(3\) 0 0
\(4\) 2.07216 + 1.25056i 1.03608 + 0.625278i
\(5\) 1.27054 0.0493029i 0.568204 0.0220489i 0.246927 0.969034i \(-0.420579\pi\)
0.321277 + 0.946985i \(0.395888\pi\)
\(6\) 0 0
\(7\) 4.39851 + 0.687914i 1.66248 + 0.260007i 0.914757 0.404004i \(-0.132382\pi\)
0.747723 + 0.664011i \(0.231147\pi\)
\(8\) −0.606370 0.642715i −0.214384 0.227234i
\(9\) 0 0
\(10\) −2.60120 0.616496i −0.822572 0.194953i
\(11\) −0.0413646 0.302842i −0.0124719 0.0913103i 0.983512 0.180843i \(-0.0578825\pi\)
−0.995984 + 0.0895324i \(0.971463\pi\)
\(12\) 0 0
\(13\) 1.95043 2.84380i 0.540952 0.788727i −0.453793 0.891107i \(-0.649930\pi\)
0.994745 + 0.102380i \(0.0326456\pi\)
\(14\) −8.52104 3.87329i −2.27734 1.03518i
\(15\) 0 0
\(16\) −1.39012 2.63908i −0.347530 0.659770i
\(17\) 6.95270 3.49177i 1.68628 0.846880i 0.694412 0.719577i \(-0.255664\pi\)
0.991864 0.127303i \(-0.0406319\pi\)
\(18\) 0 0
\(19\) 0.466686 + 8.01269i 0.107065 + 1.83824i 0.443199 + 0.896423i \(0.353843\pi\)
−0.336134 + 0.941814i \(0.609120\pi\)
\(20\) 2.69443 + 1.48672i 0.602492 + 0.332441i
\(21\) 0 0
\(22\) −0.0869667 + 0.636709i −0.0185414 + 0.135747i
\(23\) −1.39733 + 3.61918i −0.291364 + 0.754652i 0.707487 + 0.706727i \(0.249829\pi\)
−0.998851 + 0.0479255i \(0.984739\pi\)
\(24\) 0 0
\(25\) −3.37311 + 0.262179i −0.674623 + 0.0524358i
\(26\) −5.55385 + 4.66024i −1.08920 + 0.913948i
\(27\) 0 0
\(28\) 8.25415 + 6.92605i 1.55989 + 1.30890i
\(29\) −2.53701 1.81334i −0.471110 0.336729i 0.321030 0.947069i \(-0.395971\pi\)
−0.792140 + 0.610340i \(0.791033\pi\)
\(30\) 0 0
\(31\) −2.85491 + 3.27137i −0.512757 + 0.587555i −0.950180 0.311701i \(-0.899101\pi\)
0.437423 + 0.899256i \(0.355891\pi\)
\(32\) 1.70176 + 7.85622i 0.300832 + 1.38880i
\(33\) 0 0
\(34\) −16.0510 + 3.15231i −2.75272 + 0.540616i
\(35\) 5.62241 + 0.657166i 0.950361 + 0.111081i
\(36\) 0 0
\(37\) 1.50445 + 2.02083i 0.247331 + 0.332223i 0.908400 0.418102i \(-0.137305\pi\)
−0.661069 + 0.750325i \(0.729897\pi\)
\(38\) 3.57246 16.4923i 0.579529 2.67541i
\(39\) 0 0
\(40\) −0.802107 0.786701i −0.126824 0.124388i
\(41\) 0.728308 2.82746i 0.113743 0.441576i −0.886014 0.463659i \(-0.846536\pi\)
0.999756 + 0.0220836i \(0.00703000\pi\)
\(42\) 0 0
\(43\) −6.63437 6.02037i −1.01173 0.918098i −0.0150828 0.999886i \(-0.504801\pi\)
−0.996650 + 0.0817879i \(0.973937\pi\)
\(44\) 0.293007 0.679266i 0.0441724 0.102403i
\(45\) 0 0
\(46\) 4.87077 6.54258i 0.718156 0.964651i
\(47\) 0.229710 + 0.263218i 0.0335066 + 0.0383943i 0.769945 0.638111i \(-0.220284\pi\)
−0.736438 + 0.676505i \(0.763494\pi\)
\(48\) 0 0
\(49\) 12.2079 + 3.91431i 1.74399 + 0.559188i
\(50\) 6.97985 + 1.37080i 0.987099 + 0.193860i
\(51\) 0 0
\(52\) 7.59793 3.45368i 1.05364 0.478940i
\(53\) −0.771083 + 4.37303i −0.105916 + 0.600682i 0.884934 + 0.465716i \(0.154203\pi\)
−0.990850 + 0.134965i \(0.956908\pi\)
\(54\) 0 0
\(55\) −0.0674864 0.382735i −0.00909987 0.0516079i
\(56\) −2.22499 3.24412i −0.297327 0.433513i
\(57\) 0 0
\(58\) 4.11614 + 5.10322i 0.540476 + 0.670085i
\(59\) −2.57549 + 1.05221i −0.335301 + 0.136985i −0.539596 0.841924i \(-0.681423\pi\)
0.204296 + 0.978909i \(0.434510\pi\)
\(60\) 0 0
\(61\) 10.2081 6.16060i 1.30701 0.788784i 0.319688 0.947523i \(-0.396422\pi\)
0.987321 + 0.158739i \(0.0507429\pi\)
\(62\) 7.62689 5.01629i 0.968617 0.637069i
\(63\) 0 0
\(64\) 0.635797 10.9162i 0.0794747 1.36453i
\(65\) 2.33790 3.70933i 0.289981 0.460086i
\(66\) 0 0
\(67\) 5.48432 3.91995i 0.670016 0.478899i −0.194895 0.980824i \(-0.562437\pi\)
0.864911 + 0.501926i \(0.167375\pi\)
\(68\) 18.7738 + 1.45921i 2.27665 + 0.176955i
\(69\) 0 0
\(70\) −11.0173 4.50107i −1.31682 0.537980i
\(71\) 0.934287 + 3.12074i 0.110879 + 0.370363i 0.995361 0.0962123i \(-0.0306728\pi\)
−0.884481 + 0.466576i \(0.845488\pi\)
\(72\) 0 0
\(73\) −4.31382 + 1.02239i −0.504895 + 0.119662i −0.475167 0.879896i \(-0.657612\pi\)
−0.0297280 + 0.999558i \(0.509464\pi\)
\(74\) −1.90779 4.94130i −0.221776 0.574415i
\(75\) 0 0
\(76\) −9.05327 + 17.1872i −1.03848 + 1.97151i
\(77\) 0.0263870 1.36051i 0.00300708 0.155044i
\(78\) 0 0
\(79\) 9.02377 8.85045i 1.01525 0.995754i 0.0152622 0.999884i \(-0.495142\pi\)
0.999991 + 0.00412970i \(0.00131453\pi\)
\(80\) −1.89632 3.28453i −0.212015 0.367221i
\(81\) 0 0
\(82\) −3.06932 + 5.31621i −0.338949 + 0.587077i
\(83\) 0.101470 + 0.393932i 0.0111378 + 0.0432397i 0.973718 0.227759i \(-0.0731399\pi\)
−0.962580 + 0.270999i \(0.912646\pi\)
\(84\) 0 0
\(85\) 8.66155 4.77924i 0.939477 0.518381i
\(86\) 10.0431 + 15.9345i 1.08297 + 1.71826i
\(87\) 0 0
\(88\) −0.169559 + 0.210220i −0.0180750 + 0.0224095i
\(89\) −2.03708 + 6.80431i −0.215930 + 0.721256i 0.779555 + 0.626334i \(0.215445\pi\)
−0.995485 + 0.0949220i \(0.969740\pi\)
\(90\) 0 0
\(91\) 10.5353 11.1667i 1.10440 1.17059i
\(92\) −7.42149 + 5.75209i −0.773744 + 0.599697i
\(93\) 0 0
\(94\) −0.316855 0.662646i −0.0326811 0.0683467i
\(95\) 0.987994 + 10.1575i 0.101366 + 1.04213i
\(96\) 0 0
\(97\) −11.4753 0.445293i −1.16514 0.0452127i −0.551066 0.834462i \(-0.685779\pi\)
−0.614073 + 0.789249i \(0.710470\pi\)
\(98\) −22.5194 14.8112i −2.27480 1.49616i
\(99\) 0 0
\(100\) −7.31751 3.67499i −0.731751 0.367499i
\(101\) −0.205424 10.5916i −0.0204405 1.05391i −0.859894 0.510473i \(-0.829470\pi\)
0.839453 0.543432i \(-0.182875\pi\)
\(102\) 0 0
\(103\) −2.96955 2.30158i −0.292598 0.226781i 0.455716 0.890125i \(-0.349383\pi\)
−0.748314 + 0.663344i \(0.769136\pi\)
\(104\) −3.01043 + 0.470823i −0.295197 + 0.0461680i
\(105\) 0 0
\(106\) 4.02737 8.42253i 0.391173 0.818069i
\(107\) 12.7984 + 4.65825i 1.23727 + 0.450330i 0.876082 0.482162i \(-0.160148\pi\)
0.361190 + 0.932492i \(0.382371\pi\)
\(108\) 0 0
\(109\) 0.649699 0.236471i 0.0622299 0.0226498i −0.310718 0.950502i \(-0.600569\pi\)
0.372948 + 0.927852i \(0.378347\pi\)
\(110\) −0.0791034 + 0.813254i −0.00754221 + 0.0775407i
\(111\) 0 0
\(112\) −4.29900 12.5643i −0.406217 1.18721i
\(113\) 3.77910 3.42935i 0.355508 0.322606i −0.474608 0.880197i \(-0.657410\pi\)
0.830116 + 0.557591i \(0.188274\pi\)
\(114\) 0 0
\(115\) −1.59694 + 4.66722i −0.148915 + 0.435221i
\(116\) −2.98940 6.93020i −0.277559 0.643453i
\(117\) 0 0
\(118\) 5.80975 0.679062i 0.534831 0.0625127i
\(119\) 32.9835 10.5757i 3.02360 0.969477i
\(120\) 0 0
\(121\) 10.5071 2.92484i 0.955189 0.265895i
\(122\) −24.1492 + 6.72240i −2.18637 + 0.608617i
\(123\) 0 0
\(124\) −10.0069 + 3.20857i −0.898643 + 0.288138i
\(125\) −10.5873 + 1.23747i −0.946955 + 0.110683i
\(126\) 0 0
\(127\) 1.90220 + 4.40979i 0.168793 + 0.391306i 0.981526 0.191331i \(-0.0612804\pi\)
−0.812733 + 0.582637i \(0.802021\pi\)
\(128\) −2.23791 + 6.54054i −0.197805 + 0.578107i
\(129\) 0 0
\(130\) −6.82665 + 6.19485i −0.598737 + 0.543325i
\(131\) −4.74803 13.8766i −0.414837 1.21241i −0.933857 0.357646i \(-0.883580\pi\)
0.519020 0.854762i \(-0.326297\pi\)
\(132\) 0 0
\(133\) −3.45932 + 35.5649i −0.299961 + 3.08387i
\(134\) −13.3183 + 4.84745i −1.15052 + 0.418756i
\(135\) 0 0
\(136\) −6.46012 2.35129i −0.553951 0.201622i
\(137\) −7.61387 + 15.9231i −0.650497 + 1.36040i 0.267402 + 0.963585i \(0.413835\pi\)
−0.917899 + 0.396814i \(0.870116\pi\)
\(138\) 0 0
\(139\) −0.742794 + 0.116171i −0.0630030 + 0.00985349i −0.185942 0.982561i \(-0.559534\pi\)
0.122939 + 0.992414i \(0.460768\pi\)
\(140\) 10.8287 + 8.39290i 0.915194 + 0.709329i
\(141\) 0 0
\(142\) −0.132809 6.84762i −0.0111451 0.574639i
\(143\) −0.941900 0.473040i −0.0787656 0.0395576i
\(144\) 0 0
\(145\) −3.31278 2.17885i −0.275111 0.180944i
\(146\) 9.31381 + 0.361418i 0.770816 + 0.0299112i
\(147\) 0 0
\(148\) 0.590307 + 6.06889i 0.0485230 + 0.498860i
\(149\) −5.05212 10.5656i −0.413886 0.865569i −0.998526 0.0542762i \(-0.982715\pi\)
0.584640 0.811293i \(-0.301236\pi\)
\(150\) 0 0
\(151\) −13.9478 + 10.8104i −1.13506 + 0.879736i −0.993904 0.110252i \(-0.964834\pi\)
−0.141154 + 0.989988i \(0.545081\pi\)
\(152\) 4.86689 5.15860i 0.394757 0.418418i
\(153\) 0 0
\(154\) −0.820525 + 2.74075i −0.0661198 + 0.220856i
\(155\) −3.46600 + 4.29717i −0.278396 + 0.345157i
\(156\) 0 0
\(157\) −0.227240 0.360541i −0.0181358 0.0287743i 0.836796 0.547514i \(-0.184426\pi\)
−0.854932 + 0.518740i \(0.826401\pi\)
\(158\) −23.2671 + 12.8382i −1.85103 + 1.02136i
\(159\) 0 0
\(160\) 2.54950 + 9.89777i 0.201556 + 0.782487i
\(161\) −8.63587 + 14.9578i −0.680602 + 1.17884i
\(162\) 0 0
\(163\) 0.971273 + 1.68229i 0.0760760 + 0.131767i 0.901554 0.432667i \(-0.142428\pi\)
−0.825478 + 0.564435i \(0.809094\pi\)
\(164\) 5.04507 4.94817i 0.393954 0.386387i
\(165\) 0 0
\(166\) 0.0165846 0.855095i 0.00128721 0.0663683i
\(167\) −6.65976 + 12.6433i −0.515348 + 0.978364i 0.479553 + 0.877513i \(0.340799\pi\)
−0.994901 + 0.100851i \(0.967843\pi\)
\(168\) 0 0
\(169\) 0.399308 + 1.03423i 0.0307160 + 0.0795565i
\(170\) −20.2380 + 4.79650i −1.55219 + 0.367875i
\(171\) 0 0
\(172\) −6.21868 20.7718i −0.474170 1.58384i
\(173\) −6.34793 2.59341i −0.482624 0.197174i 0.123812 0.992306i \(-0.460488\pi\)
−0.606436 + 0.795132i \(0.707402\pi\)
\(174\) 0 0
\(175\) −15.0170 1.16722i −1.13518 0.0882333i
\(176\) −0.741722 + 0.530151i −0.0559094 + 0.0399617i
\(177\) 0 0
\(178\) 7.96237 12.6332i 0.596805 0.946895i
\(179\) 0.396395 6.80583i 0.0296279 0.508692i −0.950550 0.310572i \(-0.899479\pi\)
0.980178 0.198120i \(-0.0634835\pi\)
\(180\) 0 0
\(181\) −4.77429 + 3.14010i −0.354870 + 0.233402i −0.714409 0.699728i \(-0.753304\pi\)
0.359539 + 0.933130i \(0.382934\pi\)
\(182\) −27.6345 + 16.6775i −2.04841 + 1.23622i
\(183\) 0 0
\(184\) 3.17340 1.29648i 0.233946 0.0955776i
\(185\) 2.01111 + 2.49338i 0.147859 + 0.183317i
\(186\) 0 0
\(187\) −1.34505 1.96113i −0.0983599 0.143412i
\(188\) 0.146827 + 0.832695i 0.0107084 + 0.0607306i
\(189\) 0 0
\(190\) 3.72585 21.1303i 0.270301 1.53295i
\(191\) 5.62928 2.55882i 0.407320 0.185150i −0.199663 0.979865i \(-0.563985\pi\)
0.606983 + 0.794715i \(0.292380\pi\)
\(192\) 0 0
\(193\) 4.91108 + 0.964505i 0.353507 + 0.0694266i 0.366314 0.930491i \(-0.380620\pi\)
−0.0128064 + 0.999918i \(0.504077\pi\)
\(194\) 22.9914 + 7.37189i 1.65068 + 0.529271i
\(195\) 0 0
\(196\) 20.4017 + 23.3778i 1.45727 + 1.66984i
\(197\) 5.70503 7.66319i 0.406467 0.545980i −0.551007 0.834501i \(-0.685756\pi\)
0.957474 + 0.288521i \(0.0931636\pi\)
\(198\) 0 0
\(199\) 2.17258 5.03661i 0.154010 0.357036i −0.823690 0.567040i \(-0.808088\pi\)
0.977701 + 0.210004i \(0.0673477\pi\)
\(200\) 2.21386 + 2.00897i 0.156544 + 0.142056i
\(201\) 0 0
\(202\) −5.55567 + 21.5684i −0.390896 + 1.51755i
\(203\) −9.91162 9.72125i −0.695659 0.682298i
\(204\) 0 0
\(205\) 0.785944 3.62832i 0.0548927 0.253413i
\(206\) 4.71696 + 6.33598i 0.328646 + 0.441448i
\(207\) 0 0
\(208\) −10.2163 1.19412i −0.708375 0.0827972i
\(209\) 2.40728 0.472774i 0.166515 0.0327024i
\(210\) 0 0
\(211\) 2.63348 + 12.1575i 0.181296 + 0.836957i 0.973857 + 0.227163i \(0.0729452\pi\)
−0.792560 + 0.609794i \(0.791252\pi\)
\(212\) −7.06652 + 8.09734i −0.485331 + 0.556127i
\(213\) 0 0
\(214\) −23.2960 16.6510i −1.59248 1.13824i
\(215\) −8.72608 7.32205i −0.595114 0.499360i
\(216\) 0 0
\(217\) −14.8078 + 12.4252i −1.00522 + 0.843478i
\(218\) −1.44925 + 0.112645i −0.0981556 + 0.00762925i
\(219\) 0 0
\(220\) 0.338788 0.877483i 0.0228411 0.0591599i
\(221\) 3.63085 26.5825i 0.244237 1.78813i
\(222\) 0 0
\(223\) −17.6050 9.71405i −1.17892 0.650501i −0.232235 0.972660i \(-0.574604\pi\)
−0.946686 + 0.322158i \(0.895592\pi\)
\(224\) 2.08082 + 35.7263i 0.139031 + 2.38707i
\(225\) 0 0
\(226\) −9.58785 + 4.81520i −0.637774 + 0.320302i
\(227\) 11.2474 + 21.3527i 0.746519 + 1.41723i 0.903040 + 0.429556i \(0.141330\pi\)
−0.156521 + 0.987675i \(0.550028\pi\)
\(228\) 0 0
\(229\) −8.99223 4.08747i −0.594223 0.270108i 0.0940401 0.995568i \(-0.470022\pi\)
−0.688264 + 0.725461i \(0.741627\pi\)
\(230\) 5.86596 8.55277i 0.386790 0.563953i
\(231\) 0 0
\(232\) 0.372902 + 2.73013i 0.0244822 + 0.179242i
\(233\) −3.77592 0.894910i −0.247369 0.0586275i 0.105061 0.994466i \(-0.466496\pi\)
−0.352430 + 0.935838i \(0.614644\pi\)
\(234\) 0 0
\(235\) 0.304834 + 0.323105i 0.0198852 + 0.0210770i
\(236\) −6.65268 1.04046i −0.433053 0.0677282i
\(237\) 0 0
\(238\) −72.7688 + 2.82376i −4.71690 + 0.183037i
\(239\) 16.1160 + 9.72608i 1.04246 + 0.629128i 0.931142 0.364657i \(-0.118814\pi\)
0.111318 + 0.993785i \(0.464493\pi\)
\(240\) 0 0
\(241\) −7.39774 2.05930i −0.476531 0.132651i 0.0215759 0.999767i \(-0.493132\pi\)
−0.498107 + 0.867116i \(0.665971\pi\)
\(242\) −22.9305 −1.47403
\(243\) 0 0
\(244\) 28.8569 1.84738
\(245\) 15.7037 + 4.37142i 1.00327 + 0.279280i
\(246\) 0 0
\(247\) 23.6967 + 14.3010i 1.50778 + 0.909953i
\(248\) 3.83369 0.148765i 0.243439 0.00944656i
\(249\) 0 0
\(250\) 22.1415 + 3.46287i 1.40035 + 0.219011i
\(251\) −14.2128 15.0647i −0.897105 0.950876i 0.101930 0.994792i \(-0.467498\pi\)
−0.999035 + 0.0439158i \(0.986017\pi\)
\(252\) 0 0
\(253\) 1.15384 + 0.273465i 0.0725414 + 0.0171926i
\(254\) −1.36646 10.0042i −0.0857392 0.627722i
\(255\) 0 0
\(256\) −4.14909 + 6.04952i −0.259318 + 0.378095i
\(257\) 5.95450 + 2.70665i 0.371431 + 0.168836i 0.590824 0.806800i \(-0.298803\pi\)
−0.219393 + 0.975637i \(0.570408\pi\)
\(258\) 0 0
\(259\) 5.22719 + 9.92358i 0.324802 + 0.616621i
\(260\) 9.48323 4.76265i 0.588125 0.295367i
\(261\) 0 0
\(262\) 1.79292 + 30.7833i 0.110767 + 1.90180i
\(263\) 4.77665 + 2.63564i 0.294541 + 0.162521i 0.623500 0.781823i \(-0.285710\pi\)
−0.328959 + 0.944344i \(0.606698\pi\)
\(264\) 0 0
\(265\) −0.764091 + 5.59414i −0.0469378 + 0.343645i
\(266\) 27.0588 70.0840i 1.65908 4.29713i
\(267\) 0 0
\(268\) 16.2665 1.26433i 0.993635 0.0772314i
\(269\) 14.2376 11.9467i 0.868079 0.728405i −0.0956136 0.995419i \(-0.530481\pi\)
0.963693 + 0.267014i \(0.0860369\pi\)
\(270\) 0 0
\(271\) 2.60029 + 2.18190i 0.157956 + 0.132541i 0.718340 0.695692i \(-0.244902\pi\)
−0.560384 + 0.828233i \(0.689347\pi\)
\(272\) −18.8802 13.4947i −1.14478 0.818238i
\(273\) 0 0
\(274\) 24.3991 27.9583i 1.47400 1.68902i
\(275\) 0.218926 + 1.01068i 0.0132018 + 0.0609461i
\(276\) 0 0
\(277\) 11.8391 2.32513i 0.711345 0.139704i 0.176065 0.984378i \(-0.443663\pi\)
0.535280 + 0.844675i \(0.320206\pi\)
\(278\) 1.56998 + 0.183504i 0.0941612 + 0.0110059i
\(279\) 0 0
\(280\) −2.98689 4.01209i −0.178501 0.239768i
\(281\) −4.81522 + 22.2295i −0.287252 + 1.32610i 0.574389 + 0.818583i \(0.305240\pi\)
−0.861640 + 0.507519i \(0.830563\pi\)
\(282\) 0 0
\(283\) 1.16736 + 1.14494i 0.0693924 + 0.0680596i 0.734086 0.679056i \(-0.237611\pi\)
−0.664694 + 0.747116i \(0.731438\pi\)
\(284\) −1.96666 + 7.63505i −0.116700 + 0.453057i
\(285\) 0 0
\(286\) 1.64105 + 1.48917i 0.0970372 + 0.0880566i
\(287\) 5.14852 11.9356i 0.303908 0.704537i
\(288\) 0 0
\(289\) 25.9958 34.9184i 1.52916 2.05402i
\(290\) 5.48134 + 6.28092i 0.321875 + 0.368828i
\(291\) 0 0
\(292\) −10.2175 3.27611i −0.597934 0.191720i
\(293\) −30.2253 5.93605i −1.76578 0.346788i −0.798791 0.601608i \(-0.794527\pi\)
−0.966988 + 0.254821i \(0.917984\pi\)
\(294\) 0 0
\(295\) −3.22040 + 1.46385i −0.187499 + 0.0852287i
\(296\) 0.386563 2.19231i 0.0224685 0.127425i
\(297\) 0 0
\(298\) 4.27566 + 24.2484i 0.247682 + 1.40467i
\(299\) 7.56682 + 11.0327i 0.437601 + 0.638037i
\(300\) 0 0
\(301\) −25.0399 31.0446i −1.44327 1.78938i
\(302\) 34.3455 14.0317i 1.97636 0.807432i
\(303\) 0 0
\(304\) 20.4974 12.3702i 1.17560 0.709481i
\(305\) 12.6661 8.33059i 0.725256 0.477008i
\(306\) 0 0
\(307\) −0.327766 + 5.62752i −0.0187066 + 0.321179i 0.975954 + 0.217977i \(0.0699459\pi\)
−0.994660 + 0.103202i \(0.967091\pi\)
\(308\) 1.75607 2.78620i 0.100061 0.158758i
\(309\) 0 0
\(310\) 9.44298 6.74944i 0.536325 0.383342i
\(311\) 10.2693 + 0.798194i 0.582319 + 0.0452614i 0.365274 0.930900i \(-0.380975\pi\)
0.217045 + 0.976162i \(0.430358\pi\)
\(312\) 0 0
\(313\) −6.21727 2.54003i −0.351421 0.143571i 0.195614 0.980681i \(-0.437330\pi\)
−0.547035 + 0.837110i \(0.684244\pi\)
\(314\) 0.256981 + 0.858375i 0.0145023 + 0.0484409i
\(315\) 0 0
\(316\) 29.7667 7.05484i 1.67451 0.396866i
\(317\) −7.94335 20.5738i −0.446143 1.15554i −0.955502 0.294985i \(-0.904685\pi\)
0.509359 0.860554i \(-0.329883\pi\)
\(318\) 0 0
\(319\) −0.444214 + 0.843320i −0.0248712 + 0.0472169i
\(320\) 0.269607 13.9009i 0.0150715 0.777082i
\(321\) 0 0
\(322\) 25.9249 25.4269i 1.44474 1.41699i
\(323\) 31.2232 + 54.0802i 1.73731 + 3.00910i
\(324\) 0 0
\(325\) −5.83344 + 10.1038i −0.323581 + 0.560459i
\(326\) −1.01874 3.95500i −0.0564229 0.219047i
\(327\) 0 0
\(328\) −2.25888 + 1.24640i −0.124726 + 0.0688207i
\(329\) 0.829309 + 1.31579i 0.0457213 + 0.0725418i
\(330\) 0 0
\(331\) −2.89324 + 3.58705i −0.159027 + 0.197162i −0.851610 0.524175i \(-0.824374\pi\)
0.692584 + 0.721338i \(0.256472\pi\)
\(332\) −0.282371 + 0.943186i −0.0154971 + 0.0517640i
\(333\) 0 0
\(334\) 20.6174 21.8532i 1.12813 1.19575i
\(335\) 6.77480 5.25086i 0.370147 0.286885i
\(336\) 0 0
\(337\) −5.52792 11.5607i −0.301125 0.629750i 0.694872 0.719133i \(-0.255461\pi\)
−0.995997 + 0.0893836i \(0.971510\pi\)
\(338\) −0.225653 2.31991i −0.0122739 0.126187i
\(339\) 0 0
\(340\) 23.9248 + 0.928392i 1.29751 + 0.0503491i
\(341\) 1.10880 + 0.729269i 0.0600449 + 0.0394921i
\(342\) 0 0
\(343\) 23.1549 + 11.6288i 1.25025 + 0.627899i
\(344\) 0.153503 + 7.91458i 0.00827633 + 0.426726i
\(345\) 0 0
\(346\) 11.3951 + 8.83187i 0.612605 + 0.474804i
\(347\) −29.6350 + 4.63483i −1.59089 + 0.248811i −0.887094 0.461589i \(-0.847279\pi\)
−0.703798 + 0.710400i \(0.748514\pi\)
\(348\) 0 0
\(349\) 3.49423 7.30757i 0.187042 0.391165i −0.787191 0.616709i \(-0.788465\pi\)
0.974233 + 0.225544i \(0.0724160\pi\)
\(350\) 29.7579 + 10.8310i 1.59063 + 0.578941i
\(351\) 0 0
\(352\) 2.30880 0.840335i 0.123060 0.0447900i
\(353\) 1.94929 20.0405i 0.103750 1.06665i −0.788478 0.615063i \(-0.789131\pi\)
0.892229 0.451584i \(-0.149141\pi\)
\(354\) 0 0
\(355\) 1.34091 + 3.91897i 0.0711683 + 0.207997i
\(356\) −12.7303 + 11.5522i −0.674706 + 0.612263i
\(357\) 0 0
\(358\) −4.64012 + 13.5613i −0.245238 + 0.716736i
\(359\) −3.83515 8.89089i −0.202412 0.469243i 0.786529 0.617553i \(-0.211876\pi\)
−0.988941 + 0.148310i \(0.952617\pi\)
\(360\) 0 0
\(361\) −45.1139 + 5.27306i −2.37441 + 0.277529i
\(362\) 11.4405 3.66823i 0.601297 0.192798i
\(363\) 0 0
\(364\) 35.7954 9.96434i 1.87619 0.522273i
\(365\) −5.43049 + 1.51168i −0.284245 + 0.0791250i
\(366\) 0 0
\(367\) −2.14957 + 0.689233i −0.112207 + 0.0359777i −0.360899 0.932605i \(-0.617530\pi\)
0.248692 + 0.968583i \(0.419999\pi\)
\(368\) 11.4938 1.34343i 0.599154 0.0700311i
\(369\) 0 0
\(370\) −2.66755 6.18408i −0.138679 0.321495i
\(371\) −6.39988 + 18.7044i −0.332265 + 0.971082i
\(372\) 0 0
\(373\) 2.71982 2.46810i 0.140827 0.127793i −0.598550 0.801086i \(-0.704256\pi\)
0.739377 + 0.673292i \(0.235120\pi\)
\(374\) 1.61859 + 4.73051i 0.0836954 + 0.244609i
\(375\) 0 0
\(376\) 0.0298851 0.307245i 0.00154121 0.0158450i
\(377\) −10.1050 + 3.67793i −0.520435 + 0.189423i
\(378\) 0 0
\(379\) −25.0947 9.13373i −1.28903 0.469168i −0.395620 0.918414i \(-0.629470\pi\)
−0.893408 + 0.449246i \(0.851693\pi\)
\(380\) −10.6552 + 22.2834i −0.546600 + 1.14312i
\(381\) 0 0
\(382\) −12.8444 + 2.00884i −0.657179 + 0.102781i
\(383\) −14.8230 11.4887i −0.757420 0.587045i 0.158993 0.987280i \(-0.449175\pi\)
−0.916413 + 0.400235i \(0.868928\pi\)
\(384\) 0 0
\(385\) −0.0335511 1.72989i −0.00170992 0.0881632i
\(386\) −9.40327 4.72250i −0.478614 0.240369i
\(387\) 0 0
\(388\) −23.2218 15.2732i −1.17891 0.775379i
\(389\) −28.8247 1.11853i −1.46147 0.0567116i −0.704286 0.709916i \(-0.748733\pi\)
−0.757182 + 0.653204i \(0.773424\pi\)
\(390\) 0 0
\(391\) 2.92214 + 30.0423i 0.147779 + 1.51930i
\(392\) −4.88673 10.2197i −0.246817 0.516175i
\(393\) 0 0
\(394\) −15.8758 + 12.3047i −0.799812 + 0.619901i
\(395\) 11.0287 11.6898i 0.554916 0.588177i
\(396\) 0 0
\(397\) 10.7257 35.8263i 0.538307 1.79807i −0.0617229 0.998093i \(-0.519660\pi\)
0.600030 0.799978i \(-0.295155\pi\)
\(398\) −7.24016 + 8.97639i −0.362916 + 0.449946i
\(399\) 0 0
\(400\) 5.38095 + 8.53746i 0.269047 + 0.426873i
\(401\) 3.41840 1.88620i 0.170707 0.0941921i −0.395458 0.918484i \(-0.629414\pi\)
0.566165 + 0.824292i \(0.308426\pi\)
\(402\) 0 0
\(403\) 3.73479 + 14.4994i 0.186043 + 0.722265i
\(404\) 12.8197 22.2044i 0.637806 1.10471i
\(405\) 0 0
\(406\) 14.5943 + 25.2781i 0.724304 + 1.25453i
\(407\) 0.549762 0.539203i 0.0272507 0.0267273i
\(408\) 0 0
\(409\) 0.497713 25.6619i 0.0246103 1.26890i −0.760415 0.649438i \(-0.775004\pi\)
0.785025 0.619464i \(-0.212650\pi\)
\(410\) −3.63759 + 6.90580i −0.179648 + 0.341053i
\(411\) 0 0
\(412\) −3.27514 8.48282i −0.161355 0.417919i
\(413\) −12.0522 + 2.85642i −0.593048 + 0.140555i
\(414\) 0 0
\(415\) 0.148345 + 0.495505i 0.00728195 + 0.0243234i
\(416\) 25.6607 + 10.4835i 1.25812 + 0.513998i
\(417\) 0 0
\(418\) −5.14234 0.399694i −0.251520 0.0195497i
\(419\) 14.1957 10.1465i 0.693507 0.495689i −0.179275 0.983799i \(-0.557375\pi\)
0.872782 + 0.488110i \(0.162314\pi\)
\(420\) 0 0
\(421\) −5.35349 + 8.49389i −0.260913 + 0.413967i −0.950731 0.310016i \(-0.899666\pi\)
0.689818 + 0.723982i \(0.257690\pi\)
\(422\) 1.52068 26.1090i 0.0740255 1.27097i
\(423\) 0 0
\(424\) 3.27817 2.15609i 0.159202 0.104709i
\(425\) −22.5368 + 13.6010i −1.09319 + 0.659746i
\(426\) 0 0
\(427\) 49.1382 20.0752i 2.37797 0.971506i
\(428\) 20.6950 + 25.6578i 1.00033 + 1.24022i
\(429\) 0 0
\(430\) 13.5458 + 19.7503i 0.653237 + 0.952442i
\(431\) 2.16526 + 12.2798i 0.104297 + 0.591498i 0.991499 + 0.130116i \(0.0415351\pi\)
−0.887202 + 0.461382i \(0.847354\pi\)
\(432\) 0 0
\(433\) −6.71847 + 38.1024i −0.322869 + 1.83108i 0.201375 + 0.979514i \(0.435459\pi\)
−0.524244 + 0.851568i \(0.675652\pi\)
\(434\) 36.9977 16.8175i 1.77595 0.807268i
\(435\) 0 0
\(436\) 1.64200 + 0.322479i 0.0786376 + 0.0154439i
\(437\) −29.6515 9.50738i −1.41842 0.454800i
\(438\) 0 0
\(439\) 7.64117 + 8.75581i 0.364693 + 0.417892i 0.906230 0.422785i \(-0.138947\pi\)
−0.541537 + 0.840677i \(0.682157\pi\)
\(440\) −0.205067 + 0.275453i −0.00977620 + 0.0131317i
\(441\) 0 0
\(442\) −22.3418 + 51.7940i −1.06269 + 2.46359i
\(443\) 0.240326 + 0.218084i 0.0114182 + 0.0103615i 0.677697 0.735341i \(-0.262978\pi\)
−0.666279 + 0.745703i \(0.732114\pi\)
\(444\) 0 0
\(445\) −2.25272 + 8.74561i −0.106789 + 0.414582i
\(446\) 30.1809 + 29.6012i 1.42911 + 1.40166i
\(447\) 0 0
\(448\) 10.3060 47.5777i 0.486912 2.24784i
\(449\) −9.28761 12.4754i −0.438310 0.588752i 0.526998 0.849866i \(-0.323317\pi\)
−0.965308 + 0.261114i \(0.915910\pi\)
\(450\) 0 0
\(451\) −0.886401 0.103605i −0.0417390 0.00487859i
\(452\) 12.1195 2.38019i 0.570053 0.111955i
\(453\) 0 0
\(454\) −10.7419 49.5901i −0.504142 2.32738i
\(455\) 12.8350 14.7072i 0.601713 0.689486i
\(456\) 0 0
\(457\) 24.5294 + 17.5325i 1.14743 + 0.820137i 0.986000 0.166746i \(-0.0533261\pi\)
0.161435 + 0.986883i \(0.448388\pi\)
\(458\) 15.9086 + 13.3489i 0.743360 + 0.623753i
\(459\) 0 0
\(460\) −9.14573 + 7.67418i −0.426422 + 0.357811i
\(461\) −33.6136 + 2.61265i −1.56554 + 0.121683i −0.830764 0.556625i \(-0.812096\pi\)
−0.734777 + 0.678309i \(0.762713\pi\)
\(462\) 0 0
\(463\) −7.72979 + 20.0207i −0.359234 + 0.930439i 0.628989 + 0.777414i \(0.283469\pi\)
−0.988222 + 0.153024i \(0.951099\pi\)
\(464\) −1.25881 + 9.21612i −0.0584388 + 0.427848i
\(465\) 0 0
\(466\) 7.14332 + 3.94151i 0.330908 + 0.182587i
\(467\) −2.07111 35.5596i −0.0958397 1.64550i −0.613339 0.789820i \(-0.710174\pi\)
0.517499 0.855684i \(-0.326863\pi\)
\(468\) 0 0
\(469\) 26.8194 13.4692i 1.23841 0.621951i
\(470\) −0.435248 0.826299i −0.0200765 0.0381143i
\(471\) 0 0
\(472\) 2.23797 + 1.01728i 0.103011 + 0.0468242i
\(473\) −1.54879 + 2.25820i −0.0712136 + 0.103832i
\(474\) 0 0
\(475\) −3.67495 26.9054i −0.168618 1.23450i
\(476\) 81.5728 + 19.3331i 3.73888 + 0.886131i
\(477\) 0 0
\(478\) −27.1582 28.7860i −1.24219 1.31664i
\(479\) 38.9663 + 6.09422i 1.78042 + 0.278452i 0.957231 0.289323i \(-0.0934302\pi\)
0.823184 + 0.567775i \(0.192196\pi\)
\(480\) 0 0
\(481\) 8.68116 0.336869i 0.395827 0.0153599i
\(482\) 13.8226 + 8.34197i 0.629601 + 0.379966i
\(483\) 0 0
\(484\) 25.4300 + 7.07894i 1.15591 + 0.321770i
\(485\) −14.6018 −0.663034
\(486\) 0 0
\(487\) −43.1512 −1.95537 −0.977684 0.210079i \(-0.932628\pi\)
−0.977684 + 0.210079i \(0.932628\pi\)
\(488\) −10.1494 2.82527i −0.459440 0.127894i
\(489\) 0 0
\(490\) −29.3421 17.7081i −1.32554 0.799968i
\(491\) −39.3080 + 1.52533i −1.77394 + 0.0688371i −0.904830 0.425773i \(-0.860002\pi\)
−0.869115 + 0.494611i \(0.835311\pi\)
\(492\) 0 0
\(493\) −23.9708 3.74897i −1.07959 0.168845i
\(494\) −39.9329 42.3264i −1.79667 1.90436i
\(495\) 0 0
\(496\) 12.6021 + 2.98674i 0.565849 + 0.134109i
\(497\) 1.96267 + 14.3693i 0.0880379 + 0.644551i
\(498\) 0 0
\(499\) −8.60295 + 12.5434i −0.385121 + 0.561520i −0.967972 0.251059i \(-0.919221\pi\)
0.582851 + 0.812579i \(0.301937\pi\)
\(500\) −23.4861 10.6757i −1.05033 0.477433i
\(501\) 0 0
\(502\) 20.2934 + 38.5260i 0.905738 + 1.71950i
\(503\) −25.5520 + 12.8327i −1.13931 + 0.572181i −0.915446 0.402440i \(-0.868162\pi\)
−0.223861 + 0.974621i \(0.571866\pi\)
\(504\) 0 0
\(505\) −0.783197 13.4470i −0.0348518 0.598383i
\(506\) −2.18285 1.20444i −0.0970393 0.0535440i
\(507\) 0 0
\(508\) −1.57303 + 11.5166i −0.0697918 + 0.510967i
\(509\) 0.820458 2.12504i 0.0363662 0.0941907i −0.913511 0.406814i \(-0.866640\pi\)
0.949877 + 0.312623i \(0.101208\pi\)
\(510\) 0 0
\(511\) −19.6777 + 1.52947i −0.870491 + 0.0676599i
\(512\) 22.4056 18.8005i 0.990196 0.830873i
\(513\) 0 0
\(514\) −10.5344 8.83940i −0.464652 0.389889i
\(515\) −3.88642 2.77784i −0.171256 0.122406i
\(516\) 0 0
\(517\) 0.0702117 0.0804537i 0.00308791 0.00353835i
\(518\) −4.99224 23.0468i −0.219347 1.01262i
\(519\) 0 0
\(520\) −3.80167 + 0.746624i −0.166714 + 0.0327416i
\(521\) 18.3527 + 2.14512i 0.804046 + 0.0939795i 0.508181 0.861250i \(-0.330318\pi\)
0.295865 + 0.955230i \(0.404392\pi\)
\(522\) 0 0
\(523\) 9.24118 + 12.4131i 0.404089 + 0.542785i 0.956861 0.290547i \(-0.0938374\pi\)
−0.552772 + 0.833333i \(0.686430\pi\)
\(524\) 7.51483 34.6923i 0.328287 1.51554i
\(525\) 0 0
\(526\) −8.18877 8.03148i −0.357047 0.350189i
\(527\) −8.42646 + 32.7135i −0.367062 + 1.42502i
\(528\) 0 0
\(529\) 5.88656 + 5.34177i 0.255937 + 0.232251i
\(530\) 4.70169 10.8998i 0.204229 0.473455i
\(531\) 0 0
\(532\) −51.6442 + 69.3702i −2.23906 + 3.00758i
\(533\) −6.62022 7.58593i −0.286754 0.328583i
\(534\) 0 0
\(535\) 16.4906 + 5.28751i 0.712952 + 0.228599i
\(536\) −5.84494 1.14791i −0.252463 0.0495821i
\(537\) 0 0
\(538\) −35.5730 + 16.1699i −1.53366 + 0.697135i
\(539\) 0.680444 3.85899i 0.0293088 0.166218i
\(540\) 0 0
\(541\) −1.99478 11.3130i −0.0857624 0.486383i −0.997189 0.0749210i \(-0.976130\pi\)
0.911427 0.411462i \(-0.134982\pi\)
\(542\) −4.03652 5.88538i −0.173383 0.252799i
\(543\) 0 0
\(544\) 39.2640 + 48.6797i 1.68343 + 2.08713i
\(545\) 0.813812 0.332479i 0.0348599 0.0142418i
\(546\) 0 0
\(547\) −27.5720 + 16.6398i −1.17889 + 0.711465i −0.964190 0.265214i \(-0.914557\pi\)
−0.214703 + 0.976679i \(0.568878\pi\)
\(548\) −35.6898 + 23.4736i −1.52459 + 1.00274i
\(549\) 0 0
\(550\) 0.126417 2.17049i 0.00539043 0.0925502i
\(551\) 13.3458 21.1745i 0.568549 0.902064i
\(552\) 0 0
\(553\) 45.7795 32.7212i 1.94674 1.39145i
\(554\) −25.2904 1.96572i −1.07448 0.0835155i
\(555\) 0 0
\(556\) −1.68447 0.688181i −0.0714373 0.0291854i
\(557\) 4.91838 + 16.4285i 0.208399 + 0.696100i 0.996727 + 0.0808446i \(0.0257617\pi\)
−0.788328 + 0.615255i \(0.789053\pi\)
\(558\) 0 0
\(559\) −30.0606 + 7.12449i −1.27143 + 0.301334i
\(560\) −6.08152 15.7515i −0.256991 0.665624i
\(561\) 0 0
\(562\) 22.2863 42.3095i 0.940092 1.78472i
\(563\) 0.112124 5.78111i 0.00472548 0.243645i −0.990000 0.141069i \(-0.954946\pi\)
0.994725 0.102576i \(-0.0327083\pi\)
\(564\) 0 0
\(565\) 4.63243 4.54346i 0.194888 0.191145i
\(566\) −1.71888 2.97718i −0.0722497 0.125140i
\(567\) 0 0
\(568\) 1.43922 2.49280i 0.0603883 0.104596i
\(569\) −5.48878 21.3088i −0.230102 0.893310i −0.974282 0.225331i \(-0.927654\pi\)
0.744181 0.667979i \(-0.232840\pi\)
\(570\) 0 0
\(571\) 21.2092 11.7027i 0.887577 0.489744i 0.0273326 0.999626i \(-0.491299\pi\)
0.860244 + 0.509882i \(0.170311\pi\)
\(572\) −1.36021 2.15811i −0.0568731 0.0902353i
\(573\) 0 0
\(574\) −17.1575 + 21.2720i −0.716141 + 0.887875i
\(575\) 3.76449 12.5743i 0.156990 0.524384i
\(576\) 0 0
\(577\) −18.8099 + 19.9374i −0.783068 + 0.830003i −0.988900 0.148584i \(-0.952528\pi\)
0.205832 + 0.978587i \(0.434010\pi\)
\(578\) −72.3404 + 56.0680i −3.00896 + 2.33212i
\(579\) 0 0
\(580\) −4.13984 8.65774i −0.171897 0.359493i
\(581\) 0.175327 + 1.80252i 0.00727379 + 0.0747811i
\(582\) 0 0
\(583\) 1.35623 + 0.0526280i 0.0561694 + 0.00217963i
\(584\) 3.27288 + 2.15261i 0.135433 + 0.0890755i
\(585\) 0 0
\(586\) 57.8725 + 29.0646i 2.39069 + 1.20065i
\(587\) 0.0957648 + 4.93761i 0.00395264 + 0.203797i 0.996582 + 0.0826081i \(0.0263250\pi\)
−0.992629 + 0.121189i \(0.961329\pi\)
\(588\) 0 0
\(589\) −27.5448 21.3488i −1.13496 0.879663i
\(590\) 7.34806 1.14922i 0.302515 0.0473124i
\(591\) 0 0
\(592\) 3.24176 6.77957i 0.133236 0.278639i
\(593\) −6.11543 2.22584i −0.251131 0.0914041i 0.213388 0.976968i \(-0.431550\pi\)
−0.464518 + 0.885564i \(0.653773\pi\)
\(594\) 0 0
\(595\) 41.3856 15.0631i 1.69664 0.617528i
\(596\) 2.74408 28.2116i 0.112402 1.15559i
\(597\) 0 0
\(598\) −9.10567 26.6123i −0.372359 1.08826i
\(599\) 15.9256 14.4517i 0.650703 0.590481i −0.278327 0.960486i \(-0.589780\pi\)
0.929030 + 0.370005i \(0.120644\pi\)
\(600\) 0 0
\(601\) −12.2625 + 35.8386i −0.500199 + 1.46189i 0.350666 + 0.936501i \(0.385955\pi\)
−0.850865 + 0.525385i \(0.823921\pi\)
\(602\) 33.2131 + 76.9966i 1.35367 + 3.13815i
\(603\) 0 0
\(604\) −42.4211 + 4.95832i −1.72609 + 0.201751i
\(605\) 13.2055 4.23417i 0.536880 0.172144i
\(606\) 0 0
\(607\) 9.64724 2.68549i 0.391569 0.109001i −0.0667916 0.997767i \(-0.521276\pi\)
0.458361 + 0.888766i \(0.348437\pi\)
\(608\) −62.1553 + 17.3021i −2.52073 + 0.701693i
\(609\) 0 0
\(610\) −30.3512 + 9.73172i −1.22888 + 0.394026i
\(611\) 1.19657 0.139859i 0.0484081 0.00565810i
\(612\) 0 0
\(613\) 6.03527 + 13.9913i 0.243762 + 0.565105i 0.995543 0.0943087i \(-0.0300641\pi\)
−0.751781 + 0.659413i \(0.770805\pi\)
\(614\) 3.83676 11.2134i 0.154839 0.452535i
\(615\) 0 0
\(616\) −0.890419 + 0.808012i −0.0358760 + 0.0325557i
\(617\) 7.19187 + 21.0190i 0.289534 + 0.846195i 0.991044 + 0.133535i \(0.0426330\pi\)
−0.701510 + 0.712660i \(0.747490\pi\)
\(618\) 0 0
\(619\) 0.0117882 0.121193i 0.000473808 0.00487117i −0.995063 0.0992462i \(-0.968357\pi\)
0.995537 + 0.0943750i \(0.0300853\pi\)
\(620\) −12.5560 + 4.57000i −0.504260 + 0.183535i
\(621\) 0 0
\(622\) −20.3498 7.40672i −0.815952 0.296982i
\(623\) −13.6409 + 28.5275i −0.546511 + 1.14293i
\(624\) 0 0
\(625\) 3.32270 0.519660i 0.132908 0.0207864i
\(626\) 11.1605 + 8.65008i 0.446065 + 0.345727i
\(627\) 0 0
\(628\) −0.0200016 1.03128i −0.000798150 0.0411524i
\(629\) 17.5163 + 8.79701i 0.698420 + 0.350760i
\(630\) 0 0
\(631\) 8.64926 + 5.68870i 0.344321 + 0.226464i 0.709877 0.704326i \(-0.248751\pi\)
−0.365555 + 0.930790i \(0.619121\pi\)
\(632\) −11.1601 0.433061i −0.443923 0.0172262i
\(633\) 0 0
\(634\) 4.48886 + 46.1495i 0.178275 + 1.83283i
\(635\) 2.63424 + 5.50905i 0.104537 + 0.218620i
\(636\) 0 0
\(637\) 34.9422 27.0823i 1.38446 1.07304i
\(638\) 1.37521 1.45763i 0.0544449 0.0577083i
\(639\) 0 0
\(640\) −2.52089 + 8.42037i −0.0996471 + 0.332844i
\(641\) −2.63182 + 3.26294i −0.103951 + 0.128878i −0.827668 0.561218i \(-0.810333\pi\)
0.723718 + 0.690096i \(0.242432\pi\)
\(642\) 0 0
\(643\) −1.99798 3.17001i −0.0787925 0.125013i 0.804278 0.594253i \(-0.202552\pi\)
−0.883070 + 0.469241i \(0.844528\pi\)
\(644\) −36.6005 + 20.1953i −1.44226 + 0.795805i
\(645\) 0 0
\(646\) −32.7492 127.140i −1.28850 5.00226i
\(647\) 23.3221 40.3951i 0.916887 1.58809i 0.112772 0.993621i \(-0.464027\pi\)
0.804115 0.594474i \(-0.202640\pi\)
\(648\) 0 0
\(649\) 0.425186 + 0.736444i 0.0166900 + 0.0289080i
\(650\) 17.5120 17.1756i 0.686876 0.673683i
\(651\) 0 0
\(652\) −0.0911684 + 4.70062i −0.00357043 + 0.184090i
\(653\) −17.7554 + 33.7078i −0.694822 + 1.31909i 0.242340 + 0.970191i \(0.422085\pi\)
−0.937162 + 0.348895i \(0.886557\pi\)
\(654\) 0 0
\(655\) −6.71673 17.3968i −0.262445 0.679748i
\(656\) −8.47434 + 2.00845i −0.330867 + 0.0784170i
\(657\) 0 0
\(658\) −0.937846 3.13262i −0.0365610 0.122122i
\(659\) 12.1664 + 4.97052i 0.473935 + 0.193624i 0.602567 0.798069i \(-0.294145\pi\)
−0.128631 + 0.991692i \(0.541058\pi\)
\(660\) 0 0
\(661\) −16.9129 1.31458i −0.657837 0.0511312i −0.255765 0.966739i \(-0.582327\pi\)
−0.402073 + 0.915608i \(0.631710\pi\)
\(662\) 7.88251 5.63408i 0.306363 0.218975i
\(663\) 0 0
\(664\) 0.191657 0.304085i 0.00743775 0.0118008i
\(665\) −2.64176 + 45.3574i −0.102443 + 1.75888i
\(666\) 0 0
\(667\) 10.1079 6.64805i 0.391378 0.257413i
\(668\) −29.6112 + 17.8704i −1.14569 + 0.691428i
\(669\) 0 0
\(670\) −16.6824 + 6.81553i −0.644499 + 0.263307i
\(671\) −2.28794 2.83660i −0.0883249 0.109506i
\(672\) 0 0
\(673\) −11.0433 16.1015i −0.425688 0.620669i 0.551212 0.834365i \(-0.314166\pi\)
−0.976900 + 0.213697i \(0.931450\pi\)
\(674\) 4.67833 + 26.5321i 0.180202 + 1.02198i
\(675\) 0 0
\(676\) −0.465937 + 2.64246i −0.0179206 + 0.101633i
\(677\) −41.2654 + 18.7574i −1.58596 + 0.720906i −0.996234 0.0866996i \(-0.972368\pi\)
−0.589723 + 0.807606i \(0.700763\pi\)
\(678\) 0 0
\(679\) −50.1678 9.85264i −1.92526 0.378110i
\(680\) −8.32379 2.66892i −0.319203 0.102348i
\(681\) 0 0
\(682\) −1.83463 2.10225i −0.0702515 0.0804992i
\(683\) −3.50729 + 4.71111i −0.134203 + 0.180266i −0.864145 0.503244i \(-0.832140\pi\)
0.729942 + 0.683509i \(0.239547\pi\)
\(684\) 0 0
\(685\) −8.88870 + 20.6063i −0.339620 + 0.787327i
\(686\) −40.3423 36.6087i −1.54027 1.39772i
\(687\) 0 0
\(688\) −6.66566 + 25.8777i −0.254126 + 0.986577i
\(689\) 10.9321 + 10.7221i 0.416478 + 0.408479i
\(690\) 0 0
\(691\) −0.420680 + 1.94208i −0.0160034 + 0.0738800i −0.984637 0.174613i \(-0.944133\pi\)
0.968634 + 0.248493i \(0.0799352\pi\)
\(692\) −9.91073 13.3124i −0.376749 0.506062i
\(693\) 0 0
\(694\) 62.6370 + 7.32122i 2.37767 + 0.277910i
\(695\) −0.938025 + 0.184222i −0.0355813 + 0.00698794i
\(696\) 0 0
\(697\) −4.80917 22.2016i −0.182160 0.840945i
\(698\) −11.1975 + 12.8309i −0.423831 + 0.485656i
\(699\) 0 0
\(700\) −29.6581 21.1983i −1.12097 0.801220i
\(701\) 6.38533 + 5.35793i 0.241171 + 0.202366i 0.755359 0.655311i \(-0.227462\pi\)
−0.514189 + 0.857677i \(0.671907\pi\)
\(702\) 0 0
\(703\) −15.4902 + 12.9978i −0.584224 + 0.490222i
\(704\) −3.33219 + 0.258998i −0.125587 + 0.00976136i
\(705\) 0 0
\(706\) −15.2474 + 39.4916i −0.573842 + 1.48629i
\(707\) 6.38256 46.7286i 0.240041 1.75741i
\(708\) 0 0
\(709\) 20.2204 + 11.1571i 0.759392 + 0.419015i 0.815017 0.579437i \(-0.196728\pi\)
−0.0556253 + 0.998452i \(0.517715\pi\)
\(710\) −0.506347 8.69365i −0.0190029 0.326267i
\(711\) 0 0
\(712\) 5.60846 2.81667i 0.210186 0.105559i
\(713\) −7.85041 14.9036i −0.294000 0.558146i
\(714\) 0 0
\(715\) −1.22005 0.554579i −0.0456272 0.0207401i
\(716\) 9.33247 13.6071i 0.348771 0.508520i
\(717\) 0 0
\(718\) 2.75501 + 20.1702i 0.102816 + 0.752747i
\(719\) 50.4503 + 11.9569i 1.88148 + 0.445919i 0.999670 0.0256879i \(-0.00817762\pi\)
0.881809 + 0.471607i \(0.156326\pi\)
\(720\) 0 0
\(721\) −11.4783 12.1663i −0.427475 0.453097i
\(722\) 94.3483 + 14.7558i 3.51128 + 0.549154i
\(723\) 0 0
\(724\) −13.8200 + 0.536277i −0.513615 + 0.0199306i
\(725\) 9.03303 + 5.45146i 0.335478 + 0.202462i
\(726\) 0 0
\(727\) 45.4706 + 12.6576i 1.68641 + 0.469445i 0.972905 0.231203i \(-0.0742662\pi\)
0.713507 + 0.700648i \(0.247106\pi\)
\(728\) −13.5653 −0.502763
\(729\) 0 0
\(730\) 11.8514 0.438641
\(731\) −67.1486 18.6921i −2.48358 0.691352i
\(732\) 0 0
\(733\) −31.4336 18.9703i −1.16103 0.700683i −0.200724 0.979648i \(-0.564330\pi\)
−0.960301 + 0.278965i \(0.910009\pi\)
\(734\) 4.74242 0.184028i 0.175046 0.00679258i
\(735\) 0 0
\(736\) −30.8110 4.81876i −1.13571 0.177622i
\(737\) −1.41398 1.49873i −0.0520847 0.0552066i
\(738\) 0 0
\(739\) −31.3668 7.43407i −1.15385 0.273467i −0.391215 0.920299i \(-0.627945\pi\)
−0.762632 + 0.646833i \(0.776093\pi\)
\(740\) 1.04922 + 7.68169i 0.0385703 + 0.282384i
\(741\) 0 0
\(742\) 23.5084 34.2761i 0.863021 1.25832i
\(743\) −22.8905 10.4050i −0.839771 0.381723i −0.0527187 0.998609i \(-0.516789\pi\)
−0.787052 + 0.616887i \(0.788394\pi\)
\(744\) 0 0
\(745\) −6.93986 13.1750i −0.254257 0.482694i
\(746\) −6.90037 + 3.46550i −0.252640 + 0.126881i
\(747\) 0 0
\(748\) −0.334657 5.74585i −0.0122363 0.210089i
\(749\) 53.0896 + 29.2936i 1.93985 + 1.07036i
\(750\) 0 0
\(751\) −3.73259 + 27.3274i −0.136204 + 0.997191i 0.788104 + 0.615543i \(0.211063\pi\)
−0.924308 + 0.381648i \(0.875357\pi\)
\(752\) 0.375329 0.972127i 0.0136869 0.0354498i
\(753\) 0 0
\(754\) 22.5408 1.75201i 0.820886 0.0638043i
\(755\) −17.1883 + 14.4227i −0.625547 + 0.524896i
\(756\) 0 0
\(757\) −6.23353 5.23055i −0.226561 0.190108i 0.522440 0.852676i \(-0.325022\pi\)
−0.749001 + 0.662569i \(0.769466\pi\)
\(758\) 45.6779 + 32.6486i 1.65910 + 1.18585i
\(759\) 0 0
\(760\) 5.92926 6.79418i 0.215077 0.246451i
\(761\) 2.91446 + 13.4546i 0.105649 + 0.487730i 0.999245 + 0.0388574i \(0.0123718\pi\)
−0.893596 + 0.448873i \(0.851826\pi\)
\(762\) 0 0
\(763\) 3.02038 0.593183i 0.109345 0.0214747i
\(764\) 14.8647 + 1.73744i 0.537787 + 0.0628583i
\(765\) 0 0
\(766\) 23.5455 + 31.6271i 0.850733 + 1.14273i
\(767\) −2.03106 + 9.37644i −0.0733375 + 0.338563i
\(768\) 0 0
\(769\) 0.938893 + 0.920860i 0.0338574 + 0.0332071i 0.716949 0.697125i \(-0.245538\pi\)
−0.683092 + 0.730333i \(0.739365\pi\)
\(770\) −0.907386 + 3.52269i −0.0326999 + 0.126949i
\(771\) 0 0
\(772\) 8.97038 + 8.14019i 0.322851 + 0.292972i
\(773\) −9.31617 + 21.5973i −0.335079 + 0.776801i 0.664485 + 0.747301i \(0.268651\pi\)
−0.999565 + 0.0295001i \(0.990608\pi\)
\(774\) 0 0
\(775\) 8.77226 11.7832i 0.315109 0.423265i
\(776\) 6.67207 + 7.64534i 0.239513 + 0.274452i
\(777\) 0 0
\(778\) 57.7518 + 18.5174i 2.07050 + 0.663880i
\(779\) 22.9955 + 4.51617i 0.823899 + 0.161808i
\(780\) 0 0
\(781\) 0.906444 0.412029i 0.0324351 0.0147436i
\(782\) 11.0198 62.4962i 0.394066 2.23486i
\(783\) 0 0
\(784\) −6.64031 37.6591i −0.237154 1.34497i
\(785\) −0.306494 0.446880i −0.0109393 0.0159498i
\(786\) 0 0